The game-theory tag has no wiki summary.

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**1**answer

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### Did Nash prove that every game or every symmetric game has a symmetric equilibrium?

Most references seem to state that Nash showed every symmetric game has a symmetric equilibrium point, but as far as I can tell from Nash's paper, he actually showed the much more general statement ...

**-4**

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**0**answers

51 views

### Easy Question - A function with some proprietys [closed]

I have a problem:
A group of employers {e1, e2, ..., en} with salaries {s1, s2, ..., sn}
and a number dependents {d1, d2, ..., dn} (the employer + his family, di >= 1) wants to make a contract of ...

**35**

votes

**4**answers

5k views

### Why was John Nash's 1950 Game Theory paper such a big deal?

I'm trying to understand why John Nash's 1950 2-page paper that was published in PNAS was such a big deal. Unless I'm mistaken, the 1928 paper by John von Neumann demonstrated that all n-player ...

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votes

**0**answers

166 views

### Game Theory - need references on analysis of particular game

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I ...

**1**

vote

**0**answers

23 views

### Game Theroy - A joint project problem [migrated]

I'm new to this forum and as such not sure if this is the correct place to ask for help on Game Theory. As such I am currently working out of the Introduction to Game theroy book by Martin J Osborne ...

**15**

votes

**1**answer

507 views

### Paul Erdős: Determine or estimate the number of maximal triangle-free graphs on n vertices

Among the collections of the open problems of Paul Erdős on the website of
Professor Fan Chung, there is one called "number of triangle-free graphs".
...

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votes

**0**answers

362 views

### Proof of Upper bound of price of anarchy in local connection game

I am looking at the work by Fabrikant "On a Network Connection Game" (http://webcourse.cs.technion.ac.il/236620/Spring2005/ho/WCFiles/FLMPS_netDesign.pdf). This work presents a game-theoretic ...

**4**

votes

**1**answer

89 views

### Nash Equilibrium in general graphical game

Any one has any ideas about how to compute the Nash Equilibrium in general graphical game? Especially, when the graph structure is not a tree.

**15**

votes

**6**answers

984 views

### Is a fair lottery possible?

I'm trying to come up with a scheme for a lottery where each individual has roughly the same chance of becoming the winner, regardless of the number of tickets one holds. So no individual should have ...

**1**

vote

**1**answer

133 views

### Optimum control of a probabilistic automaton

Suppose we have a probabilistic automaton and we assign a weight to each state. An "interaction strategy" would be a fixed map from states to inputs. Any interaction strategy could be used to ...

**-1**

votes

**2**answers

233 views

### Generalized Sprague-Grundy Theorem

Hey,
I know what is Sprague-Grundy theorem, but I want to know about generalized Sprague-Grundy (GSG) theorem ( which is used for games with cycles ). Apparently there seems to be very less ...

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**9**answers

2k views

### a mathematically rigorous introduction to game theory

I am looking for the best book that contains a mathematically rigorous introduction to game theory. I am a group theorist who has taken a recent interest in game theory, but I'm not sure of the best ...

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votes

**0**answers

257 views

### Coin Toss Probabilities like Penney's Game

Generate a binary number, using coin toss. Until you receive a predefined sequence. What is the probability that the number is a multiple of some k.
For example, the terminating sequence could be ...

**11**

votes

**0**answers

237 views

### A Ramsey avoidance game

Consider the following game: Given $K_n$ the complete graph on $n$ vertices, two players take turns coloring its edges. Initially no edges are colored. At his turn a player can color a prevoiusly not ...

**-1**

votes

**1**answer

129 views

### To what equal constant in the Gibbs lemma

The Gibbs lemma is broadly used in games theory and in mathematical economics (optimal distributions of resourses, Cournot competition e.t.c.). Here it is:
Lemma (Gibbs). $f_1,f_2,\ldots,f_n$ be ...

**5**

votes

**1**answer

431 views

### What can be done with computability logic that previous logic systems can't?

I've been reading a lot about computability logic lately and I'm superficially aware that it unifies classical, intuitionistic and linear logics.
What I'm seeking to know is:
Can computability logic ...

**5**

votes

**1**answer

637 views

### Algorithm on winning strategy of Winner (Simplified card game)

Here's an introduction to the ordinary Winner (card game):
http://en.wikipedia.org/wiki/Winner_(card_game)
I'm thinking about a simplification of the game.
** I've copied this problem to cstheory ...

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votes

**0**answers

184 views

### Identification of a curious function

The following question was asked on math.stackexchange, but there were no replies.
During computation of some Shapley values (details below), I encountered the following function:
$$
f\left(\sum_{k ...

**0**

votes

**1**answer

171 views

### Equilibrium of random zero-sum game,

Hi,
How to find, or at least express, the equilibrium of a zero-sum game with an $n*n$ payoff matrix (each player has $n$ strategies) and the payoff of the entry $(i,j)$ is $u(i,j)$. $u$ a random ...

**1**

vote

**3**answers

156 views

### Simulating Mixed Nash Equilibria

I have a $N$ person game where each person has a set of $M$ discrete strategies. I know from the theory that at least one mixed strategy Nash Equilibrium exists.
Can someone please tell me how do I ...

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votes

**1**answer

159 views

### How many different states of Nash equilibrium?

So there is this quite well known Prisoner's dilemma where two parties can both defect and cooperate (and get points based on their decisions). In my presently used example I take it that cooperating ...

**2**

votes

**1**answer

138 views

### Optimal auction for risk-averse seller

Consider an auction of a single unit of indivisible good. There are $n$ buyers whose values of the object is drawn independently from the uniform distribution on $[0,1]$. The buyers have interim ...

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votes

**2**answers

422 views

### Is quantum game theory reducible to classical game theory?

Quantum game theory is an extension of classical game theory to the quantum domain. It differs from classical game theory in three primary ways:
Superposed initial states,
Quantum ...

**16**

votes

**2**answers

5k views

### Lowest Unique Bid

Each of n players simultaneously choose a positive integer, and one of the players who chose [the least number of [the numbers chosen the fewest times of [the numbers chosen at least once]]] is ...

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votes

**3**answers

230 views

### Can we efficiently compute a third Nash Equilibrium, given two?

A finite, two-player, nondegenerate, symmetric game is defined by a nondegenerate $n \times n$ payoff matrix $A$. If player 1 plays strategy $i$ and player 2 plays strategy $j$, then player 1's ...

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votes

**5**answers

547 views

### $n$-in-a-row game on $\mathbb{R}^2$

For integers $n$ such that $\:3< n\:$,$\:$ what is known about the following 2-player game:
Player_1 and Player_2 take turn choosing points on $\mathbb{R}^2$ that were not previously chosen, with ...

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votes

**6**answers

3k views

### I know that you know…

A bit unsure if the following vague question has enough mathematical content to be suitable upon here. In the case, please feel free to close it.
In several circumstances of competition, a particular ...

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votes

**49**answers

15k views

### Which popular games are the most mathematical?

I consider a game to be mathematical if there is interesting mathematics (to a mathematician) involved in
the game's structure,
optimal strategies,
practical strategies,
analysis of the game ...

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votes

**2**answers

670 views

### Is there an equivalent of Heisenberg's uncertainty principle in the decision sciences ?

From memories of a quantum mechanics class and Wikipedia:
In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the ...

**1**

vote

**5**answers

749 views

### Nash Equilibrium of simple betting game [closed]

I'm trying to find the Nash Equilibrium of a simple betting game, and have come up with a very surprising result which I'd like to solicit comment on.
The game is simple: Two players each receive a ...

**2**

votes

**1**answer

142 views

### Non-Constant-Sum Blotto Game for Only 2 Players and 2 Battlefields

In the simplest asymmetric Colonel Blotto game with 2 players, dividing their given Ni soldiers (i=1,2) over 2 battlefields, what are their expected utilities, Ui (i.e., expected number of battlefield ...

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**2**answers

1k views

### Game Theory: Is there a Mixed Strategy Nash Equilibrium?

The game looks like this:
a b
A [(-12, 1) (8, 8)]
B [(15, 1), (8,-1)]
(15, 1) and (8,8) are Nash Equlibria. However, could you still mix ...

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votes

**1**answer

375 views

### M-matrix plus S-matrix is P-matrix?

I am trying to prove that a mapping has a unique fixed-point by showing that its Jacobian is a P-matrix. In this particular case the Jacobian can be decomposed as the sum of two matrices and I would ...

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votes

**3**answers

709 views

### Nim game for odd number of stones

Consider the classical Nim game with total number of stones being odd. Then the first players wins, of course, what follows from the general description of winning positions. But is there some shorter ...

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**2**answers

645 views

### An unfair game involving an odd number of pieces of chocolate

Two greedy chocolate eaters play the following game involving $n$ pieces of chocolate
and an additional parameter $\alpha$ with initial value $1$: Each player eats either $\alpha$
pieces of chocolate ...

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votes

**0**answers

134 views

### Examples of functions from matrices to real numbers with certain properties

Let $M(\mathbb{R})$ be the set of all matrices (of any size) over $\mathbb{R}$. Let $v : M(\mathbb{R}) \rightarrow \mathbb{R}$ be a function which satisfies the following 5 properties:
If ...

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votes

**1**answer

398 views

### The Chow & Robbins game ≈ 0.79295350640: improvements could come from simple statistics, or from a continuous version of the game

This question seeks help with improving a numerical estimate of the value of the Chow and Robbins game. Much about this game is unknown, such as whether its value is rational, but there are two routes ...

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**2**answers

2k views

### Simple proof of the existence of Nash equilibria for 2-person games?

Is there a nice elementary proof of the existence of Nash equilibria for 2-person games?
Here's the theorem I have in mind. Suppose $A$ and $B$ are $m \times n$ matrices of real numbers. Say a ...

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votes

**5**answers

760 views

### Algorithm to solve Sokoban-like game on graphs - move chips from one set of vertices to another

The question is close to the Sokoban game (thanks to Dima Pasechnik !), but a little different in details.
Consider a directed graph (multi-graph). Consider some set of marked chips (chip1, ...

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votes

**12**answers

3k views

### Are there any interesting connections between Game Theory and Algebraic Topology?

I've been learning game theory on my own and was just curious how it connected with previous things I've learned. So are there any interesting connections between Game Theory and Algebraic Topology? ...

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votes

**1**answer

395 views

### game theory - coin flipping question

Lets say 2 players A and B try to have the most money at the end after playing a casino game in which they have a $49\%$ chance to double a wager.
Here are the rules to the bet between A and B:
...

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votes

**9**answers

6k views

### Does War have infinite expected length?

My question concerns the (completely deterministic) card game known as War, played by seven-year-olds everywhere, such as my son Horatio, and sometimes also by others, such as their fathers.
The ...

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votes

**1**answer

394 views

### Determinantal formula for the nullspace of a singular matrix

In June 2012, Bill Press and Freeman Dyson published a remarkable paper on the iterated prisoner's dilemma. A key step in their derivation is a simple fact from linear algebra that I feel I should ...

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votes

**2**answers

211 views

### Mysterious sentence in a paper: what's the ultimate distribution of pure strategies?

Does anybody know how to interpret the sentence: For any set $T$ of mixed strategies, let $D[T]$ denote the set of probability distributions over the elements of $T$, each expressed as vector, ...

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votes

**1**answer

216 views

### Optimum Tournament Strategy

Consider a symmetric N-player game in which all players partition one total unit of
energy among individual games. The probability of winning each game is simply proportional to the spent energy ...

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votes

**0**answers

373 views

### Calculating the Shapley value in a weighted voting game.

Given a special case of WVG (Weighted Voting Game) of $a$ 1s and $b$ 2s and a quota q, $ [q:1,1,1,1..1,2,2,..2] $. I need help with calculating the Shapley value of a player with a weight of $2$ and a ...

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votes

**2**answers

498 views

### Gandhi's quote formalized [closed]

Hello,
I hope this question is appropriate for Mathoverflow. Gandhi said, "Be the change that you wish to see in the world". I don't understand anything in Game/optimization theory (I don't know ...

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**0**answers

69 views

### Computing maximum point for minimal function of a family of linear functions

Let $x \in S^n $ where $S^n = ${$ [x_1,x_2,...,x_{n+1}]\in \mathbb{R}^{n+1} \mid x \ge 0 , \sum x_i = 1 $} and let $f_i : I^n \to \mathbb{R}$ be a finite $m$-sized family of LINEAR functions such ...

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votes

**2**answers

304 views

### Uniqueness of equilibrium from infinite strategies

I took the following game from the Peter Winkler collection (chapter "Games"):
Two numbers are chosen independently at random from the uniform distribution on [0,1]. Player A then looks at the ...

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**0**answers

156 views

### Allocation game optimal strategy

There are two players, Alice and Bob. There is an initial pool of 100 dollars. Alice proposes an allocation of the dollars (real numbers, not necessarily integers), and Bob can either accept or ...